In a statement on his website, Poroshenko congratulated Ukraine's armed forces and border guards for re-establishing control over the checkpoint at Dolzhanskyi, in "the first victory since the restoration of the CTO," a reference to the government's Counterterrorist Operation. He said the armed forces and the State Border Service of Ukraine regained control over the checkpoint and combat engineers removed mines from the checkpoint and adjacent roads.

Violence flared Tuesday in Donetsk, one of the cities at the heart of the separatist unrest.

JUST WATCHED

Earlier: Ukraine announces cease-fire

MUST WATCH

JUST WATCHED

Ukraine Pres: Putin can be 'emotional'

MUST WATCH

Ukraine Pres: Putin can be 'emotional'00:51

Interior Minister Arsen Avakov, on his official Facebook page, said that militants had launched an attack on a regional police headquarters building in Donetsk, killing one police officer and badly injuring two more.

Avakov said the police were barricaded inside the building in the city of Donetsk and that the fighting was ongoing.

The Interior Ministry later said three people were seriously injured -- one woman and two special forces policemen. Three others were injured and hospitalized, the ministry said.

Police successfully fought back the attack, the ministry said on its website.

On its website, the Donetsk regional state administration said Ukrainian forces attacked the central part of Kramatorsk from the air and ground. A bus attack in Kramatorsk left four people dead and five others injured. The statement did not say which side in the conflict carried out that attack.

Yuriy Stets, information security head for the National Guard and a parliamentarian, told CNN that the National Guard had regained control of Zakotne, near Slovyansk, and were targeting two other towns.

Cease-fire hopes dashed

The fragile cease-fire expired at midnight Monday, hours after Poroshenko spoke by phone with Russian President Vladimir Putin, German Chancellor Angela Merkel and French President Francois Hollande. Poroshenko also talked on the phone with U.S. Secretary of State John Kerry.

The cease-fire -- agreed on last month amid a volatile political crisis -- raised hopes that Ukraine could be moving back from the brink of full-fledged civil war.

As part of a peace plan, Poroshenko urged the rebels to lay down their arms and engage in talks. He also called for the strengthening of Ukraine-Russia border controls, the freeing of hostages and changes to the constitution to decentralize power.

In his statement, Poroshenko said the militants had failed to take up a "unique opportunity" to support the peace plan and had instead violated the unilateral cease-fire more than 100 times.

Putin, addressing Russian diplomats in Moscow, said he regretted the decision to end the cease-fire.

"Unfortunately, President Poroshenko decided to resume a military operation. I and my EU colleagues could not convince him" of the need to settle the crisis peacefully.

Putin: 'Only on equal terms'

Putin said Russia had been obliged to annex Ukraine's Crimea region in March in order to prevent NATO forces entering, which would have created "a completely different alignment of forces."

He told the diplomats that they would "face growing pressure in defending national interests" and that "the events provoked by the West in Ukraine have become a concentrated political expression of deterrence toward Russia."

Putin also referred to Russia's tense relationship with the United States, suggesting that the current crisis was born of the West's attempts to impose its own way of doing things on the rest of the world.

"Our relationship with the United States is not the best at the moment," he said.

"We have always tried to be predictable partners, handle business on an equal basis, but in return our legal interests were partially ignored and are still ignored. Russian and U.S. contacts have a great meaning for the entire world.

"We are ready for constructive dialogue, but again I emphasize only on equal terms."

Russia's ambassador to the European Union, Vladimir Chizhov, said Tuesday that the refusal to extend the cease-fire is a "negative sign," the Russian Foreign Ministry said on Twitter.

"This makes it even harder to understand the logic of how the confirmation of the so-called 15-point peace plan correlates with the refusal to prolong truce," Chizhov was quoted as saying by state news agency ITAR-Tass.

'Enemies and invaders'

Poroshenko declared in a late-night televised address that the cease-fire was over.

In Kiev's Independence Square, known as Maidan, activists outside the presidential administration building applauded Poroshenko's stance.

"We need only military actions," a priest named Valentyn said in a Reuters interview. "We were forced by those who entered our country as enemies and invaders."

The crisis has its roots in former President Viktor Yanukovych's decision last year to shun a European Union Association Agreement and turn toward Russia instead. The move unleashed deadly strife that led to Yanukovych's ouster, Ukraine's loss of Crimea, and a pro-Russia separatist rebellion. Russia also massed troops along its western border with Ukraine.

The Association Agreement, which will bring closer trade and political ties between Ukraine and Europe, was finally signed by Poroshenko and European leaders last week.

After Monday's phone call, Poroshenko said his goal was peace but insisted it takes the participation of all parties to maintain stability, noting violations of the cease-fire by pro-Russia separatists.

The Ukrainian government "has been completely fulfilling its commitments and unilaterally complying with the ceasefire regime for 10 days and paid dozens of lives for that," he said.

Peace talks were held last week among Ukrainian government officials, pro-Russia separatists from the restive eastern Luhansk and Donetsk regions, Russian officials, and members of the Organization for Security and Cooperation in Europe.

'Bloody truce'

Activist Vadym told Reuters there was no point in continuing the cease-fire.

"There is definitely no need for an extension of the truce," he said. "Because a lot of our boys died during this truce."

Fellow activist Yulia agreed.

"Bloody military actions are better than such bloody truce," she said. "We must put an end to it once and that's all."

A statement from Putin's press office about the call said the Russian President "stressed the need to extend the cease-fire and also establish a reliable mechanism for monitoring" it.